ON LANDAUS NECESSARY DENSITY CONDITIONS FOR SAMPLING AND INTERPOLATION OF BAND-LIMITED FUNCTIONS

We give a new short proof of H. Landau's density result on necessary c onditions for the sampling and interpolation of certain entire functio ns in the case that the boundary of the spectrum has measure 0. For th e proof we adapt a method that has been recently developed by J. Raman athan and T. Steger in the context of time-frequency analysis. As a co nsequence of a general theorem for the comparison of densities we obta in several new results about the density of irregular sampling of band -limited functions with derivatives and differential operators.